Our long-term goal is to develop a predictive science (understandings) of epidemics and pathogen re-emergence and to study the evolution of pathogenic microbes which cause human infectious disease including epidemics. Specific aims include (1) To develop population genetics theory for treatinglongitudinal samples.We will study the statistical properties of various summary statistics and develop methods to simulate population samples and to compute the probability of a pattern of segregating sites. (2) To develop and evaluate statistical methods for estimating important population parameters. We will develop statistical methods to estimate population parameters such as mutation rate, effective population size, growth rate, generation time and the age of a mutation. (3) To develop statistical methods fortesting hypotheses. We will develop statistical methods to test hypotheses that are essential for understanding the mechanism of evolution, including the hypotheses of neutral mutations, constant effective population size, and no genetic differentiation between two populations. (4) To analyze molecular data from the epidemics of Group A streptococcus. We will analyze, using both existing and newly developed statistical methods, the polymorphism data on a gene called Streptococcal inhibitor of complement (sic), which is highly polymorphic and sic variants are associated with GAS epidemics. (5) To develop a user-friendly computer package for analyzing longitudinal samples incorporating newly developed statistical methods.